Gradient techniques for open‐shell restricted Hartree–Fock and multiconfiguration self‐consistent‐field methods

1979 ◽  
Vol 71 (4) ◽  
pp. 1525-1530 ◽  
Author(s):  
John D. Goddard ◽  
Nicholas C. Handy ◽  
Henry F. Schaefer
Keyword(s):  
Open Shell ◽  
Field Methods ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field

Self-consistent Field Orbital Methods

2020 ◽  
pp. 128-149
Author(s):  
Jochen Autschbach
Keyword(s):  
Density Functional ◽  
Slater Determinant ◽  
Closed Shell ◽  
Open Shell ◽  
Initial Guess ◽  
Hartree Fock ◽  
Consistent Field ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Definition Of

This chapter discusses the concepts underlying the Hartree-Fock (HF) electronic structure method. First, it is shown how the energy expectation value is calculated for a Slater determinant (SD) wavefunction in the case of orthonormal orbitals. This leads to the definition of the electron repulsion integrals (ERIs). Next, the energy is minimized subject to the orthonormality constraints. This leads to the HF equation for the orbitals. The HF orbital energies are Langrange multipliers representing the constraints. An unknown set of orbitals can be determined from an initial guess via a self-consistent field (SCF) cycle. The HF scheme is discussed for closed-shell versus open shell systems, leading to the distinction between spin restricted and unrestricted HF (RHF, UHF). Kohn-Sham density functional theory (DFT) is introduced and its approximate version is placed in the context of ab-initio versus semi-empirical quantum chemistry methods.

GEOMETRIC DIRECT MINIMIZATION OF HARTREE–FOCK CALCULATIONS INVOLVING OPEN SHELL WAVEFUNCTIONS WITH SPIN RESTRICTED ORBITALS

2002 ◽  
Vol 01 (02) ◽  
pp. 255-261 ◽  
Author(s):  
BARRY D. DUNIETZ ◽  
TROY VAN VOORHIS ◽  
MARTIN HEAD-GORDON
Keyword(s):  
Closed Shell ◽  
Open Shell ◽  
Minimization Method ◽  
Hartree Fock ◽  
Direct Inversion ◽  
Consistent Field ◽  
Direct Minimization ◽  
Self Consistent ◽  
Self Consistent Field

Recently, we have introduced a method based on geometric considerations, termed geometric direct minimization (GDM), to achieve robust convergence of self consistent field calculations. GDM was limited to calculations involving either spin-unrestricted orbitals or closed shell systems. We report the extension of the GDM method to treat open shell systems involving spin-restricted orbitals. Open shell systems pose a challenge for achieving robust convergence of the calculation. We compare the convergence using the GDM method to the convergence achieved by the well known direct inversion in the iterative space (DIIS) technique. This comparison demonstrates the ability of the GDM method to achieve robust convergence. Additionally we assess the importance of geometric considerations by comparing against an alternative direct minimization method that is not geometrically correct.

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